Real Analysis 35 | Properties for Derivatives

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This is my video series about Real Analysis. We talk about sequences, series, continuous functions, differentiable functions, and integral. I hope that it will help everyone who wants to learn about it.

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#RealAnalysis
#Mathematics
#Calculus
#LearnMath
#Integrals
#Derivatives

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[rajinfootonchuriquen]

What a great proof of the product rule, very easy and simple. In wikipedia there is a one adding 0s to the definition, which make it more long and tedious

[ahmedamr]

Great video as always! One question:
Let f(x) be a function that is equal to 1 at x=0 and zero elsewhere. According to the first line in the video, wouldn't f(x) be differentiable at x=0 since the limit of the quotient exists?

[Hold_it]

Thanks a lot for another amazing Video! :D

[dipankarroy]

Will it be the last video of Real Analysis of this playlist?

[diegoharo]

At 1:04 you establish that lim_{x-> x_0} \delta_{f, x_0}(x) needs to exist with a specific value \delta_{f, x_0}(x_0), but in the first implication the requirement for differentiability is just that lim_{x-> x_0} \delta_{f, x_0}(x) exists. Why these two stamens are equivalent ? I think that the statement at 1:04 requires more (a limit whit a specific value) and the first stament requires just the limit exists. What am I missing ?

[synaestheziac]

Can you explain the last step of the proof the the product rule in a little more detail? Specifically, why does the term with both deltas equal zero?

[zoedesvl]

So serious version of differentiation is taught AFTER uniform convergence? Never seen any order like this. Is this what German universities do?

[FraserIland]

Please, change the title. This is part 35!!!